Two-group method

For the core region, the two-group diffusion equations are then [cf. equations (3.30) and (3.31)] as follows  

Since the reflector contains no fissile or fertile material, = 0 and p = 1 and the equations become as follows  

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Various methods have been proposed for the evaluation of D as a function of penetrant concentration from sorption measurements. They all are applicable only for sorption data of the Fickian type, and may be classified into two groups. Methods belonging to one group utilize data for the initial slope of the reduced sorption curve, while the ones belonging to the other group resort to rates at which M (<) approaches the equilibrium value Since little work has yet been done to adapt the approach-to-equihbrium data for concentration-dependent D, the subsequent discussion will be confined to methods of the former group only. 

The determination of the area under a peak—i.e., the absolute intensity of a particular gamma energy—is not as straightforward as the assignment of energy, because the area under a peak includes contributions from other gammas. The methods that have been developed for the determination of the area can be classified into two groups methods that treat the data (i.e., counts per channel) directly, and methods that fit a known function to the data. 

Buckling, was derived from flux distributions measured with Mn (10% Ni) foils at cell-boundary positions. An improved two-group method of analysis was used for the radial distribution . 

The strictly one-velocity calculations, methods 1 and 4, are seen to give much smaller critical radii than the others this indicates that the fast leakage is quite important in this system. Calculations 2 and 3 give identical results because of the large size of the bare core. It is interesting to note the comparative accuracy of the migration-area calculation, 5, which predicts, in this case, very nearly the same result as the two-group method. 

It is interesting to note that this result is identical in form to the criticality condition for the bare reactor derived previously by the standard two-group method of Sec. 8.4b [cf. Eqs. (8.155)], since (8.349) may also be written... 

The symbol 2 ° denotes the thermal absorption cross sections of the nonfuel components of the core and the thermal absorption cross section of the fuel. Thus the present method permits a direct solution for Nf and avoids entirely the trial-and-error computations required for the standard two-group method of Sec. 8.4. It should be evident from the procedure outlined above that the computational effort involved in the Feynman-Welton two-group model is only a small fraction of that required in the standard method. This fact may be more clearly demonstrated by considering a numerical example. 

Compute k for a reflected spherical reactor which has an active core radius R 37.2 cm and a spherical shell reflector of thickness 20 cm. For this calculation use (1) the material composition described for the reactor in Prob. 4.8, in the case Nm/Nf = 15,500 (2) nuclear cross sections for fuel and moderator given in Prob. 4.8 (3) the two-group method. 

Principles and Characteristics Absorbance methods can be separated into two groups methods that measure transmission, including conventional spectrophotometry, and those that measure the power absorbed by the sample, the... 

If the reactor core size is small, the two-group method does not adequately treat leakage of fast neutrons for this case two-group results may... 

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